Bubble Size Measurement in Large Bubble Columns at High Void Fraction By an Original Method of Spatial Cross-Correlation Between Optical Probes
Bubble size measurement
in large bubble columns at high void fraction by an original method of spatial cross-correlation
between optical probes
Introduction
Bubble columns are commonly used
in industrial applications due to the simplicity of the equipment and its
efficiency in heat and mass transfer. However, the hydrodynamics of bubble
columns is very complex (1) and the detailed description of phase velocities,
turbulence and mixing properties still represents a scientific challenge. The
use of CFD models is limited by the lack of physical closing laws concerning
turbulence, bubble sizes and their velocity distributions
in heterogeneous regimes. As an example of these limitations we can consider the
drag force which is directly dependent from bubble size.
The present work aims
to build an extensive database concerning bubble size that will be obtained in
different bubble columns up to 1m in diameter. An original method of spatial
cross correlation of optical probes signals has been developed to determine mean
horizontal bubble diameter.
Methodology
In the literature,
numerous techniques to measure bubble size can be found. One of these
techniques is the chemical method (2). In this technique the bubble size is
deduced from the monitoring of a well-known kinetic. However this method is
sensible to a set of chemical and physical properties. Hence, apply this
technique in large bubble columns can be very challenging. Some authors(3) used
photographic images taken from outside of the column. However, this technique
is most adequate to rectangular columns or for low void fractions conditions,
since the optical access is limited to bubbles near to the walls. The optical probes are
another measuring technique widely used in hydrodynamic studies of bubble flows
which is able to measure bubble chords and velocities(4) . However, they are
very well suited for only quasi one-dimensional flows. The objective of this
work is to exploit these sensors in more complex bubbly flows, such as those
encountered in bubble columns in the heterogeneous regime. To determine the mean horizontal bubble size in
such flow conditions, we considered the evolution of the cross-correlation
between the signals from two monofiber optical probes as a function of the
distance between the probe tips. In practice, two optical probes are placed
side by side at the same height in the bubble column, at a given horizontal
distance. The operation is repeated for various distances between probes (Figure
1).
The cross-correlation measures
the similarity of the two signals (5). In the case of single bubble-probes
interaction, the measured value is 1 when both signals are identical (no
distance between probes) and close to 0 for a distance larger than the bubble
horizontal diameter (the same bubble cannot be measured by both probes at the
same time t). Hence, some information related to the horizontal bubble size can
be extracted from the shape of the cross-correlation curve as a function of
probes distances.
To better understand how to
extract such information, a theoretical model was considered for an idealized
bubbly flow. The cross-correlation was calculated based on a probabilistic
approach for a monodispersed gas flow. Since the bubble shape can vary with the
phase composition and the flow conditions, the bubble is discretized as an
ellipsoid that can be defined by the ratio of horizontal diameter to vertical
diameter. This method was developed for two ellipsoids: a prolate and an oblate
(Figure 2). The cross-correlation curves were calculated considering a
probe crisscrossing the whole bubble volume with the second probe at a given
horizontal distance from the first probe. These calculations have been done for
several bubble sizes. A correlation was found between the initial slope of
cross-correlation curve and the mean horizontal diameter, for each bubble shape.
Using the initial slope of the experimental curves of the cross-correlation
evolution with the probes distances (Figure 1), the mean horizontal
diameter has been determined. However, preliminary results showed that for
large probe distances, the cross-correlation increases with the void fraction,
as can be seen in Figure 1. This increase of the cross-correlation value
can be related to the detection of different bubbles at the same time by both
probes. In order to avoid this effect the initial slope cross-correlation is
measured for smallest probe distance (1 mm).
to validate the bubble size measurements obtained with the optical probes.
Since the experiments were carried at high void fraction conditions (up to 35%)
there is no optical access to the inner flow from the outside of the column.
The endoscope is used as a lens inserted radially in the column that can
explore all the column diameter. The perturbation on the flow due to the
presence of the endoscope was studied through experiments where the optical
probe was placed in the focal plane of the endoscope. The results showed
identical chord distributions with or without the endoscope.
Results and
discussion
validated through experiments carried out in the 0.15 m diameter column at different
elevation in the column. The mean horizontal bubble diameter was determined by
both methods: the spatial cross correlation and the endoscope. The results show
a good agreement between both methods in all gas superficial velocity range
(from 1.6 cm/s up to 16 cm/s), as can be seen in Figure 3 for an
elevation of 15 cm from the gas distributor. Moreover, in the heterogeneous
regime, there is a wide bubble size distribution. Therefore the mean horizontal
diameter measured by the cross correlation method was compared with the bubble
size distribution measured with the endoscopic method. As can be seen (Figure
4), for a gas superficial velocity of 16 cm/s (heterogeneous regime) the
mean horizontal diameter calculated by the cross-correlation is representative
of the bubble size distribution visually measured. normal"> justify;line-height:normal"> font-family:"Times New Roman","serif"'>Further work is currently in progress to
characterize the bubble size population through radial and axial profiles in
all column scales (0.15 m, 0.4 m and 1 m diameter) at a wide range of gas
superficial velocities (up to 30 cm/s). These measurements will allow to
understand the evolution of bubble size population along the column and
consequentially describe the break-up and coalescence phenomena. The data
obtained at 1 m diameter column will be used to improve the scale-up of a
bubble column reactor. normal">
References
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Vazquez, G., Cancela, M. A., Riverol, C.,
Alvarez, E., & Navaza, J. M., Industrial & engineering chemistry
research, 39(7), (2000), 2541-2547. line-height:normal"> color:black'>(3)
Wilkinson, P. M., Haringa, H., & Van
Dierendonck, L. L., Chemical Engineering Science, 49(9), (1994), 1417-1427 line-height:normal"> color:black'>(4)
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Cartellier, E. Barrau, I.J.M.F., 24.8, (1998) ,1265-1294 line-height:normal"> color:black'>(5)
color:black'>J.S. Bendat, A. G. Piersol, Random data: Analysis and Measurements
Procedures, fourth ed., Wiley, Chichester,1971 normal"> normal"> normal;page-break-after:avoid">
Figure 1
normal"> normal"> normal;page-break-after:avoid">Figure 2
Figure 3
Figure 4